An invariant of a pair of almost commuting unbounded operators (Q1966245)

Let \(A,B\) be symmetric operators with a common dense domain in a Hilbert space. Denote by \(C\) the closure of the operator \(A+iB\). It is assumed that the operator \((I-C^*C)^{-1}\) is compact, and the closure of the image of \(C\) has a finite codimension. The author constructs a \(K\)-theoretic integer-valued invariant \(\omega (A,B)\) which equals 0, if \(A\) and \(B\) commute, and 1, if they have a non-zero scalar commutator. \(\omega (A,B)\) is stable under small perturbations of \(A,B\).